Computational Studies on the Kinetics and Mechanisms for NH
3Reactions with ClOx
(x )
0-4) Radicals
Z. F. Xu and M. C. Lin*
Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: August 21, 2006; In Final Form: NoVember 9, 2006
Kinetics and mechanisms for NH3reactions with ClOx(x ) 0-4) radicals have been investigated at the G2M
level of theory in conjunction with statistical theory calculations. The geometric parameters of the species and stationary points involved in the reactions have been optimized at the B3LYP/6-311+G(3df,2p) level of theory. Their energetics have been further refined with the G2M method. The results show that the H-abstraction process is the most favorable channel in each reaction and the barriers predicted in decreasing order are OClO > ClO > Cl > ClO3> ClO4. All reactions were found to occur by hydrogen-bonding complexes; the rate constants for these complex metathetical processes have been calculated in the temperature range 200-2000 K by the microcanonical VTST and/or RRKM theory (for ClO4+ NH3) with Eckart tunneling and multiple reflection corrections. The predicted rate constants are in good agreement with the available experimental data.
I. Introduction
The reactions of NH3with chain-carriers such as ClOx(x )
0-4) radicals play a pivotal role in the propulsion kinetics of the systems containing ammonium perchlorate (AP), a widely used propellant at present.1These reactions may also be relevant to the chemistry of stratosphere and the explosion caused by ammonium perchlorate at the Pacific Engineering and Produc-tion Company (PEPCON) facility,2where some of these species are present.
In 1974, Clyne and Watson3studied mass spectrometrically the kinetics of rapid bimolecular reactions involving ClO (X2Π, V ) 0) radicals at 298 K using molecular beam sampling from a discharge-flow system. They found that the ClO radical is unreactive toward a range of singlet ground state molecules up to 670 K and estimated that the upper limit for the NH3+ ClO rate constant at 670 K is 1× 10-15 cm3 molecule-1 s-1. In 1977, Westenberg and DeHaas4reported their measurement for the NH3+ Cl f NH2+ HCl reaction with the rate constant of 1.23× 10-13cm3molecule-1s-1at 298 K and 19.6-43.8 Torr argon pressure by the flash photolysis-resonance fluorescence technique. Recently, Gao et al.5measured the rate constant for Cl + NH3f HCl + NH2over 290-570 K by the time-resolved resonance fluorescence technique. The rate constant was fitted by the expression k(NH3 + Cl) ) (1.08 ( 0.05) × 10-11 exp[-(2.74 ( 0.04 kcal mol-1)/RT] cm3molecule-1s-1. They also characterized the potential energy surface of this reaction with the composite G3B3, CBS-QB3, and MPWB1K density functional theory. To our knowledge, no other measurements nor theoretical studies on the kinetics and mechanisms for the ClOx radical reactions with NH3 have been reported. These
reactions are in fact very relevant to the understanding and simulation of AP propulsion chemistry.
In the present study, the G2M method6has been employed to investigate the five reaction systems of NH3+ ClOx (x )
0-4), and their rate constants were also calculated and compared with the available experimental values.
II. Computational Methods
The geometric parameters of the species and stationary points related to the title reactions were optimized at the B3LYP/ 6-311+G(3df,2p) level of theory,7and their vibrational frequen-cies were also calculated at this level. For more accurate evaluation of the energetic parameters, higher-level single-point energy calculations of the stationary points were carried out by the modified Gaussian-2 (G2M) theory,6based on the optimized geometries at the B3LYP/6-311+G(3df,2p) level of theory. The G2M(CC2) method calculates the base energy at the PMP4/ 6-311G(d,p) level of theory and improves it with the expanded basis set and coupled cluster corrections as well as a “higher level correction (HLC)”. All ab initio calculations were carried out with Gaussian 03 program.8
The rate constants for the five reactions were calculated by the VARIFLEX code9based on the microcanonical variational transition state (VTST) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory10 for processes which occur by stable inter-mediates. The component rates were evaluated at the E/J-resolved level, and the pressure dependence was treated by one-dimensional master equation calculations using the Boltzmann probability of the complex for the J-distribution. For the barrierless association/decomposition process, the fitted Morse function, V(R) ) De{1 - exp[-β(R - Re)]}2, was used to represent the minimum potential energy path (MEP) as will be discussed later. Here, Deis the bonding energy excluding zero-point vibrational energy for an association reaction, R is the reaction coordinate (i.e., the distance between the two bonding atoms), and Re is the equilibrium value of R at the stable intermediate structure. For the ClO4 + NH3 reaction which occurs via two rather deep prereaction and postreaction com-plexes (vide infra), we have also employed the ChemRate code of Mokrushin et al.11to corroborate the predicted rate constant by the Variflex program.9
* Corresponding author. E-mail: chemmcl@emory.edu. NSC Distin-guished Visiting Professor at National Chiao Tung University, Hsinchu, Taiwan.
10.1021/jp065397t CCC: $37.00 © 2007 American Chemical Society Published on Web 01/04/2007
III. Results and Discussion
A. Mechanisms of NH3+ ClOx(x ) 0-4) Reactions. The
optimized geometries of the intermediate complexes and transi-tion states at the B3LYP/ 6-311+G(3df,2p) level of theory are shown in Figure 1; all their Cartesian coordinates and vibrational frequencies are placed in Table S1 of the Supporting Informa-tion. The vibrational frequencies and moments of inertia of reactants and some of their intermediate complexes and transi-tion states used in the rate constant calculatransi-tion are listed in Table 1. The potential energy diagrams of the five reactions, obtained at the G2M//B3LYP/6-311+G(3df,2p) level of theory, are presented in Figure 2. Otherwise stated, all the energies cited below are the G2M values relative to those of the reactants. In addition, the spin-orbit correction, -0.83 kcal/mol, is included for the Cl atom12in the potential energy diagram for the NH3 + Cl reaction.
NH3 + Cl. As shown in Figures 1 and 2, there are two
possibilities for Cl atom to attack the NH3molecule. In the first case, Cl approaches the side of the H atoms in NH3to form an NH3...Cl hemibonded complex (LM1) with C3Vsymmetry; the Cl-H separation is 2.595 Å. LM1 lies 3.6 kcal/mol below the reactants; it can eliminate an HCl molecule via TS1 with a 7.8 kcal/mol barrier above LM1. On the product side, another
H-bonded complex H2N‚‚‚HCl (LM2) was located, which is 4.0 kcal/mol lower than the final products, NH2+ HCl. Also, at the B3LYP/6-311+G(3df,2p) level of theory, the energy of LM1 is 12.0 kcal/mol below that of reactants, which is 8.4 kcal/ mol greater than that at the G2M level. This extra stability may be caused by overestimating the electron correlation energy of the hemibonded complex by the density functional theory. In the second case, Cl approaches the N atom of NH3to form a more stable intermediate complex Cl‚‚‚NH3(LM3) with the binding energy of 7.1 kcal/mol and the Cl-N bonding distance of 2.432 Å. However, the further decomposition of LM3 to NH2-Cl + H needs to pass TS2 with a much higher potential barrier of 48.7 kcal/mol.
From Figure 2, the heats of reaction for the formation of NH2 + HCl and NH2Cl + H are predicted to be 4.6 and 46.8 kcal/ mol, respectively. On the basis of the heats of formation for NH3, NH2, Cl, HCl, and H tabulated by Chase13in 1998, the heat of reaction of NH3+ Cl f NH2+ HCl is 4.8 ( 1.5 kcal/ mol. The predicted value lies within the experimental error range. Also, on the basis of the two values of the heat of formation of NH2Cl given by Livett et al.,14 17.7 kcal/mol (obtained from 16 kcal/ mol at 298 K based on the heats of formation of NH2+and Cl) and 13.7 kcal/mol (obtained from
Figure 1. Geometric parameters (lengths in ånstroms and angles in degrees) of the reactants, intermediate complexes, and transition states optimized
12 kcal/mol at 298 K using bond energy data obtained in their experiment) at 0 K, the heats of reaction for NH3+ Cl f H + NH2Cl are estimated to be 50.0 and 46.0 kcal/mol, respectively.
Our predicted value is 3.2 kcal/mol less than the former and is 0.8 kcal/mol higher than the latter. It is thus reasonable to employ the G2M method for elucidation and prediction of the kinetics and mechanisms of the NH3+ ClOxreactions.
Comparing the PES of NH3+ Cl, the geometric parameters of the transition state and complexes are basically in agreement with those optimized by Gao et al.5at the MPWB1K/6-31+G-(2df,2p) level of theory, and the energies of TS1, LM2, and LM3 are 2.5, 1.1, and 4.4 kcal/mol higher than theirs, respectively. Howerver, they did not report the structure of the entrance complex (LM1) for the NH2+ HCl channel.
NH3+ ClO. In this reaction, there are two possible reaction
channels as shown in Figure 2. The first one is hydrogen atom abstraction from NH3by oxygen atom of ClO via a hydrogen-bond complex ClO‚‚‚HNH2(LM4) and transition state (TS3) to another H-bonding complex ClOH‚‚‚NH2 (LM5). LM4 is predicted to have a binding energy of 1.3 kcal/mol, and TS3 and LM5 lie above the reactants at 13.2 and 4.1 kcal/mol, respectively. The complex ClOH‚‚‚NH2 can therefore easily decompose to the products NH2+ HOCl followed by H‚‚‚N bond breaking. Although LM5 can connect with the products NH2Cl + HO via TS4 with Cl atom attacking N atom, their formation is not expected to be important because of the much higher barrier of TS4 (36 kcal/mol).
The second reaction channel is the approaching of the O atom of ClO toward the N atom of NH3via TS5 with the Cl-O bond lengthening concertedly to give the complex LM6. The potential barrier of this step is 28.4 kcal/mol, which is greater than that of TS3 by 15.2 kcal/mol. LM6 is a four-membered ring structure with both weak Cl-O and Cl-H bonds. So, the Cl atom can be eliminated directly from LM6 to form NH3O + Cl. In addition, the HCl molecule can be formed exothermically from LM6 via a much lower barrier at TS6, 4.3 kcal/mol above LM6 or 15.2 kcal/ mol above the ClO + NH3reactants. This direct NH3oxidation process cannot compete with the H-abstraction reaction producing HOCl in view of the high barrier at TS5. NH3+ OClO. Both reactants NH3and OClO can first form a four-membered ring complex (LM7) with 2.7 kcal/mol binding energy; the complex has a loose structure because of the long O‚‚‚H and Cl‚‚‚N separations in LM7 (see Figure 1). LM7 can undergo H-abstraction reaction via TS7 with a 30.5 kcal/mol barrier to form the complex H2N‚‚‚HOClO (LM8) and, in principle, can also undergo O-abstraction by NH3 directly producing NH3O + ClO via TS9 with a much higher barrier of
TABLE 1: Vibrational Frequencies and Moments of Inertia for the Reactants, Some Intermediates, and Transition States of the NH3+ ClOx(x ) 0-4) Reactions Computed at the B3LYP/6-311+G(3df,2p) Level of Theory
species moments of inertia (au) frequencies (cm-1) NH3(1A1) 6.0, 6.0, 9.5 1022, 1665, 1665, 3481, 3599, 3599 ClO (2Π 1) 97.3, 97.3 861 OClO (2B 1) 35.2, 182.4, 217.7 450, 965, 1116 ClO3(2A1) 179.3, 179.3, 340.0 471, 471, 564, 921, 1078, 1078 ClO4(2B1) 297.4, 318.6, 342.3 375, 385, 414, 549, 573, 647, 903, 1161, 1258 LM1 10.6, 268.3, 268.3 223, 371, 384, 398, 1580, 1581, 3544, 3736, 3737 LM2 4.7, 424.0, 428.8 162, 175, 198, 607, 629, 1520, 2550, 3395, 3490 LM4 82.8, 647.8, 721.7 36, 56, 92, 122, 213, 868, 1037, 1664, 1673, 3470, 3585, 3595 LM5 76.9, 543.7, 620.6 30, 75, 217, 252, 293, 733, 746, 1442, 1527, 3401, 3410, 3498 LM7 134.3, 687.4, 812.1 46, 60, 65, 99, 186, 233, 456, 960, 1066, 1103, 1664, 1667, 3475, 3589, 3590 LM8 197.1, 612.2, 731.8 30, 84, 104, 226, 274, 344, 358, 665, 861, 965, 1412, 1525, 3266, 3405, 3501 LM9 344.0, 558.9, 558.9 89, 91, 133, 172, 258, 288, 479, 479, 526, 766, 893, 1008, 1008, 1607, 1608, 3466, 3648, 3648 LM10 311.4, 723.8, 760.8 19, 57, 82, 227, 263, 336, 394,442, 543, 671, 818, 1036, 1158, 1382, 1518, 3074, 3407, 3506 LM12 339.7, 761.9, 770.5 30, 98, 126, 287, 388, 413, 425,439, 486, 586,587, 600, 759, 1004, 1190, 1204, 1572, 1590, 3509, 3698, 3720 LM13 339.8, 948.6, 964.1 25, 33, 68, 231, 303, 368, 414, 444, 571, 582, 586, 747, 902, 1038, 1231, 1262, 1477, 1525, 2961, 3416, 3513 TS1 6.7, 327.7, 330.6 i319, 347, 429, 740, 911, 1414, 1589, 3411, 3508 TS3 61.1, 456.8, 514.0 i1519, 137, 140, 415, 552, 676, 772, 1233, 1548, 1592, 3446, 3537 TS7 162.1, 598.2, 681.1 i740, 75, 95, 151, 364, 437, 532, 683, 977, 1076, 1268, 1505, 1588, 3436, 3533 TS11 281.9, 578.6, 635.5 i1170, 57, 142, 220, 400, 438,462, 514, 607, 680, 830, 968, 1114, 1370, 1483, 1594, 3470, 3576 TS13 331.6, 867.9, 876.1 i1182, 32, 108, 161, 305, 409, 420, 495, 558, 589, 612, 672, 844, 014, 1177, 1221, 1227, 1549, 1628, 3476, 3594
Figure 2. Schematic energy diagrams (in kcal/mol units) computed
at the G2M//B3LYP/6-311+G(3df,2p) level of theory.
49.5 kcal/mol. The latter process apparently cannot compete with the former due to its high barrier. LM8 is an N‚‚‚H hydrogen-bonded complex lying slightly below TS7; it can dissociate readily to NH2+ HOClO and, in principle, also to NH2OCl + OH via a very high barrier at TS8, 53.2 kcal/mol, by a concerted dual-bond breaking process. In addition, a five-membered ring transition state TS10 can directly connect the reactants NH3+ OClO with the lowest energy products NH2O + HOCl. The potential barrier of TS10, 50.4 kcal/mol, is much higher than that of TS7 (30.5 kcal/mol), however, although it is the most exothermic process (∆H ) -19.4 kcal/mol) in the system.
NH3 + ClO3. Similar to the NH3 + Cl reaction, two prereaction complexes can be formed by H-O and N-Cl bondings giving LM9 and LM11, respectively. Both have C3V structures with energies slightly below the reactants by 0.3 and 4.9 kcal/mol, respectively, as shown in Figure 2. From LM9, the shortening of one of the three H‚‚‚O bonds with the concurrent lengthening of the associated H-N bond at TS11 gives rise to the H-abstraction product LM10, an N‚‚‚H-bonding complex, H2N‚‚‚HOClO2. LM10 can further fragment to produce the final products NH2+ HOClO2with an overall 6.7 kcal/mol endothermicity. The energy of TS11 is 2.1 kcal/mol while that of LM10 is -1.7 kcal/mol. This H-abstraction reaction can take place readily.
Another reaction channel is from LM11 to products NH3O + OClO via the oxygen abstraction transition state TS12 with a 24.3 kcal/mol barrier. Because TS12 is about 12 times greater than TS11 in energy, this redox process is kinetically irrelevant. NH3+ ClO4. Because of the C2Vsymmetry of ClO4in the ground electronic state (2B1), it can only form one intermediate complex (LM12) with NH3as seen in Figure 2. The prereaction complex has a 11.3 kcal/mol binding energy. Similar to the NH3-ClO2 system, both H- and O-abstraction reactions can ensue from LM12. H-abstraction occurs via TS13 to give a stable H2N‚‚‚HOClO3complex (LM13, -14.3 kcal/mol below the reactants) and the final products NH2+ HOClO3. Because of the small abstraction barrier and the high stabilities of both LM12 and LM13, TS13 lies below the reactants by as much as 8.3 kcal/mol, or 3.0 and 6.1 kcal/mol above LM12 and LM13, respectively. The reaction producing NH2 + HOClO3 is exothermic (∆H ) -3.1 kcal/mol), and it can take place readily. The barrier for O-transfer from ClO4to NH3via TS14 is 18.0 kcal/mol, which is much greater than that for the H-abstraction process. Thus, the direct oxidation of NH3to NH3O by ClO4is unimportant.
From the above discussions of the five reaction mechanisms, we can conclude that H-abstraction is the most favorable path in each reaction; the amidogen radical (NH2) is therefore the main product in this series of reactions. Comparing the reaction barriers for all the H-abstraction channels, the following decreasing order with OClO > ClO > Cl > ClO3> ClO4is observed. Also, from the five N‚‚‚H hydrogen-bonding com-plexes, LM2, LM5, LM8, LM10, and LM13, the N‚‚‚H bond energies are predicted to be 4.0, 6.5, 8.2, 8.4, and 11.3 kcal/ mol, respectively. Obviously, the N‚‚‚H bond strengths increase with the number of oxygen atoms in HClOx(x ) 0-4). At the
B3LYP/6-311+G(3df,2p) level of theory, the Mulliken atomic charge of N in NH2is -0.386e while those of Cl in HCl, HOCl, HOClO, HOClO2, and HOClO3are -0.220e, 0.029e, 0.528e, 0.968e, and 1.714e, respectively. Accordingly, the variation in the N‚‚‚H bond strengths may be attributed to the atomic charges of Cl in HClOx. The more positive the Mulliken atomic charge
of Cl in HClOxis, the stronger the N‚‚‚H bond in the complex
H2N‚‚‚HClOxbecomes.
B. Rate Constant Calculations. As discussed in the above section, the hydrogen abstractions from NH3by ClOx(x ) 0-4)
take place by complex-forming metathetical mechanisms in-volving H-bonding prereaction and postreaction intermediates:
The rate constants of these processes were calculated by microcanonical VTST and RRKM theory (for reaction 5), and the contributions from other channels are reasonably neglected. The VTST calculations were carried out with the unified statistical formulation of Miller15including both tunneling and multiple reflection corrections16above the shallow wells of the prereaction and postreaction complexes. For the RRKM calcula-tions, the L-J (Lennard-Jones) parameters were taken to beσ ) 3.47 Å and /k ) 114 K for argon buffer gas from the literature17andσ ) 4.20 Å and /k ) 230 K approximately for the intermediate complexes from our previous paper18on the HOOClO molecular intermediate. The minimum energy paths (MEPs) for barrierless association and dissociation processes occurring without intrinsic transition states were optimized at the B3LYP/6-311+G(3df, 2p) level of theory by manually varying the key coordinates point by point for complex formation from the reactants or products. They were fitted to Morse functions to approximately represent the MEPs of the association/dissociation processes. The Morse parameters are summarized in Table 2.
As indicated above, the Eckart tunneling corrections19have been made for rate constants of the H-abstraction reactions at low temperatures. However, only NH3+ ClO and NH3+ ClO3 reactions have noticeable tunneling effects because of their larger imaginary frequencies, 1519 cm-1 at TS3 and 1170 cm-1 at TS11. Their rate constants with Eckart tunneling corrections are 91.9% and 37.3% larger at 300 K for the former and latter processes, respectively. For the NH3+ Cl reaction the correction only increases its rate constant by 1.2% at 300 K because of the smaller imaginary frequencies, 319 cm-1 at TS1. The tunneling effects on the other two reactions are negligibly small. The effects of multiple reflections above the complex-wells predicted with Miller’s method15show that the rate constants for H-abstraction reactions by ClO, OClO, and ClO4are reduced by 44.8%, 172.0%, and 59.5%, respectively, at 300 K. The rate constant of NH3+ Cl was decreased by only 17.6%, and that
TABLE 2: Morse Parameters for Association/Dissociation Processes of the Hydrogen Abstraction Channels
reaction De/kcal/mol β/Å-1 Re/Å LM1 f NH3+ Cl 4.4 1.654 2.595 LM2 f NH2+ ClO 6.0 1.423 1.890 LM5 f NH2+ HOCl 8.6 1.474 1.836 LM8 f NH2+ HOClO 10.1 1.880 1.803 LM10 f NH2+ HOClO2 10.4 1.370 1.759 LM12 f NH3+ ClO4 13.4 1.671 2.204 LM13 f NH2+ HOClO3 13.2 1.513 1.702 Cl + NH3T LM1 T TS1 T LM2 f NH2+ HCl (1) ClO + NH3T LM4 T TS3 T LM5 f NH2+ HOCl (2) OClO + NH3T LM7 T TS7 T LM8 f NH2+ HOClO (3) ClO3+ NH3T LM9 T TS10 f NH2+ HOClO2 (4) ClO4+ NH3T LM12 T TS13 T LM13 f NH2+ HOClO3 (5)
of NH3+ ClO3was not affected at 300 K. These effects stem primarily from the multiple reflections above the wells of postreaction complexes as their H-abstraction transition states are closer to the exit variational barriers leading to product formation. The effects of multiple reflection and tunneling corrections for the rate constants of the NH3 + Cl and ClO reactions are shown in Figure 3. As shown in the figure, both tunneling and multireflection effects diminish gradually with increasing temperature.
In additon, the small-curvature effect20aon the reaction path of the smallest system, NH3+ Cl, via the transition state TS1 was included to correct the hydrogen transfer rate constant. The small-curvature correction factors were predicted to be 3.99 and 1.62 at 300 and 500 K, respectively; the effect disappears at high temperatures. It can also be ignored in larger reaction systems.
Figure 4 compares the rate constants of these five reactions in the temperature range 200-2000 K. All rate constants have small positive temperature dependence and exhibit no pressure effect, except that for the NH3+ ClO4reaction which has a small negative temperature dependence with a minor pressure effect at low temperatures above 100 atm. Because of the existence of the large pre- and postreaction complexes in this reaction, we have also performed rate constant calculations at 300, 500, 800, and 1000 K temperatures using the ChemRate
code11for comparison with the values predicted by Variflex.9 The variational transition states for the barrierless association/ decomposition pocesses were determined by the canonical variational method.16a,20The results of these calculations sum-marized in Table 3 indicated that the agreement in the values obtained by both methods is quite good.
The predicted individual rate constants at atmospheric pres-sure in units of cm3molecule-1s-1can be expressed as
As mentioned in the Introduction, there are two experimental rate constant data available for the NH3+Cl reaction: k(NH3+Cl) ) 1.23 × 10-13 cm3 molecule-1 s-1 at 298 K, reported by Westenberg and DeHaas,4 and the expression k(NH3+Cl) ) (1.08 ( 0.05)× 10-11exp[-(2.74 ( 0.04 kcal mol-1)/RT] cm3 molecule-1s-1for the temperature range 290-570 K, reported by Gao et al.5 As mentioned previously, Gao et al.5 also evaluated the theoretical rate constants from the PES calculated at the MPWB1K/6-31+G(2df,2p) level of theory. Figure 3a compares these data with our predicted result. Our predicted rate cosntants are in good agreeement with the experimental data below 500 K with a small deviation noted at higher
Figure 3. Predicted rate constants with multiple reflection and tunneling corrections comparing with the experimental data: (a) k (NH3 + Cl), (b) k (NH3 + ClO). Solid line indicates rate constant with
multiple reflection and tunneling effects. Dashed line indicates rate constant without multiple reflections. Dotted line indicates rate constant without tunneling corrections. Solid circle reflects ref 3. Solid square reflects ref 4. Open circle reflects experimental data from ref 5. Dashed-dotted line shows theoretical data from ref 5.
Figure 4. Predicted rate constants for five hydrogen abstraction
reactions. Solid line shows k(NH3+ Cl). Dashed line shows k(NH3+
ClO). Dotted line shows k(NH3+ OClO). Dashed-dotted line indicates
k(NH3+ ClO3). Dashed-double-dotted line indicates k(NH3+ ClO4).
TABLE 3: Comparison of Predicted Rate Constants kC(by
ChemRate Program) and kV(by Variflex Program) in cm3
molecule-1s-1for Reaction 5: ClO4+ NH3T LM12 TTS13 T LM13 f NH2+ HOClO3 T (K) kC kV 300 2.44× 10-9 3.09× 10-9 500 1.32× 10-9 1.49× 10-9 800 3.51× 10-10 5.16× 10-10 1000 2.44× 10-10 3.78× 10-10 k(NH3+ Cl) ) 9.11 × 10-19T2.47exp(-726/T) k(NH3+ ClO) ) 1.87 × 10-24T3.85exp(-4344/T) k(NH3+ OClO) ) 1.48 × 10-20T3.05exp(-15657/T) k(NH3+ ClO3) ) 1.36× 10-14T1.01exp(-2255/T) k(NH3+ ClO4) ) 8.44× 10-1T-3.02exp(-528/T) (200-1000 K) ) 2.34 × 10-20T2.80exp(4392/T) (1000-2000 K) NH3Reactions with ClOxRadicals J. Phys. Chem. A, Vol. 111, No. 4, 2007 589
temperatures. The theoretical prediction by Gao et al. is, however, 2 times greater than their experimental values.
For the NH3+ClO reaction, only one experimental rate constant, k(NH3+ClO) e 1 × 10-15 cm3 molecule-1 s-1, describes an upper limit of the rate constant at 670 K by Clyne and Watson.3The value predicted at 670 K for this reaction, 3.04 × 10-16 cm3 molecule-1 s-1, is consistent with the experimental upper limit. For the ClO4 + NH3reaction, the exceptionally large rate constant at low temperatures (see Table 3) results from the unique combination of the following factors: (1) the high attractive potential between ClO4and NH3 (the H3N‚‚‚OClO3complex has a very large dipole moment of 6.1362 D), (2) all the transition states involved in the reaction lie below the reactants, resulting in a downhill slide from the reactants to the products (NH2+ HOClO3), and (3) the large reaction path degeneracy, 12, for the abstraction reaction.
We believe that the above rate constants for the NH3+ ClOx
(x ) 0 - 4) reactions are reasonable and may be employed for computer modeling of propellant combustion involving AP with a high degree of reliability within the temperature range specified.
IV. Conclusions
The mechanisms for a series of reactions of NH3with ClOx
(x ) 0 - 4) radicals have been studied at the G2M//B3LYP/ 6-311+G(3df,2p) level of theory in conjunction with statistical rate-theory calculations. The results of these calculations show that the H-abstraction process is the most favorable low-energy reaction channel in each of these reactions, and the predicted barriers in declining order are OClO > ClO > Cl > ClO3> ClO4. Their rate constants have been calculated in temperature range 200-2000 K by microcanonical VTST and/or RRKM theory with Eckart tunneling and multiple-reflection corrections. The results of the calculations indicate that the tunneling effects on both NH3+ ClO and ClO3reactions are significant, and the effects of multiple reflections above the wells of H-bonding complexes, primarily the postreaction complexes, in the NH3 reactions with ClO, OClO, and ClO4at low temperatures are noticeable. The predicted results (for Cl and ClO reactions) are basically in agreement with available experimental data.
Acknowledgment. This work was supported by the Office of Naval Research under Grant N00014-02-1-0133. Acknowl-edgment is also made to the Cherry L. Emerson Center of Emory University for the use of its resources, which are in part supported by a National Science Foundation grant (CHE-0079627) and an IBM Shared University Research Award. M.C.L. gratefully acknowledges the support from Taiwan’s National Science Council for a distinguished visiting profes-sorship at the Center for Interdisciplinary Molecular Science, National Chiao Tung University, Hsinchu, Taiwan.
Supporting Information Available: Geometries of all complexes and transition states. This material is available free of charge via the Internet at http://pubs.acs.org.
References and Notes
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